BITSAT2024MathematicsBinomial TheoremActual
The coefficient of the highest power of x in the expansion of (x+ x^2-1 )^8+ (x- x^2-1 )^8
Options
- A64
- B128
- C256
- D512
Correct answer
C. 256
Step-by-step solution
Since (x+ x^2-1 )^8+ (x- x^2-1 )^8 array r =2 ^8 C₀ x^8+ ^8 C₂ x^6 (x^2-1 )+ ^8 C₄ x^4 (x^2-1 )^2 . .+ ^8 C₆ x^2 (x^2-1 )^3+ ^8 C₈ x^0 (x^2-1 )^4 array So coefficient of highest power of x=2 ^8 C₀+ ^8 C₂+ ^8 C₄+ ^8 C₆+ ^8 C₈ =(1+1)^8+(1-1)^8=2^8=256